Traditionally, joints are assumed to be either pinned or fully rigid, but in reality, many behave between these two extremes giving them a semi-rigid classification. By acknowledging the semi-rigidity of nominal pin joints, steel frames can be designed as semi-continuous in which the beam bending moments are partially transmitted to the column members and the need for lateral bracing is eliminated, thus reducing material and construction costs. This thesis presents the results of numerical and theoretical studies of the behaviour of bolted endplate connections to Rectangular Hollow Section (RHS) columns using flowdrill bolts and their applications in semi-continuous frame design. Such connections exhibit significant levels of initial stiffness, strength, and deformation capacity while being more cost-effective than fully welded connections. Despite this, there is limited theoretical work carried out that allows such connections to be designed using analytical methods. In addition, there are no standardised connection design tables like that for open section columns (SCI, 1995), thereby inhibiting their adoption in practice. In this thesis, newly derived equations for initial stiffness that have a greatly improved range of validity and accuracy over existing equations are presented. Equations for bending strength of a newly derived elliptical mechanism based on yield line theory and for membrane action based on internal work principles are given. Equations for flowdrill thread stripping due to gross deformation of the RHS face are also presented thus allowing prediction of all common RHS face failure mechanisms. Equations for deformation capacity are derived thus making it possible to predict the full load-deflection behaviour of the RHS face in tension component. When combined with existing equations for bolt and endplate components, it is possible to predict the full moment-rotation behaviour of bolted endplate connections to RHS columns. Extensive parametric studies using finite element analysis (FEA) as well as validation against existing tests show that the newly derived equations can accurately predict the component-level and whole joint behaviour for a wide range of configurations. Taking advantage of the initial stiffness properties that these connections offer, a parametric study is conducted to show that connections with relatively simple detailing can offer sufficient initial stiffness and strength to enable unbraced semi-continuous design of low-rise steel frames. A hand calculation method for SLS sway in semi-continuous frames is also presented thus allowing the designer to readily carry out scheme designs without advanced software knowledge. A systematic method for the detailing of these connections for use in unbraced frame design is presented to facilitate adoption in practice.